Kurtosis Definition, Types, and Importance

Distributions with negative or positive excess kurtosis are called platykurtic distributions or leptokurtic distributions respectively. It is common to compare the excess kurtosis of a distribution to 0, which is the excess kurtosis of any univariate normal distribution. Distributions with negative excess kurtosis are said to be platykurtic, although this does not imply the distribution is “flat-topped” as is sometimes stated.

define kurtosis

In practice, however, we often subtract 3 from the calculated K values so that we would have positive K values or negative K values with respect to 3. This is because K value for a normal curve often approximates 3 and that comparisons are often made with respect to normal curves. https://1investing.in/ In this case, a positive kurtosis indicates a distribution whose data values are more concentrated around the mean than those in a normal distribution. Similarly, a negative kurtosis, in this case, indicates a distribution that is more disperse than a normal distribution.

Therefore, this tool calculates and focusses more on the “tailendness” instead of peak. Values are the standardized data values using the standard deviation defined using n rather than n− 1 in the denominator. There is no upper limit to the kurtosis of a general probability distribution, and it may be infinite. Kurtosis measures how much of a probability distribution is centered around the middle vs. the tails. Skewness instead measures the relative symmetry of a distribution around the mean.


In this tutorial titled ‘The Simplified and Complete Guide to Skewness and Kurtosis’, you will be exploring some of the different types of distortion that can occur in a normal curve. Kurtosis is a measure of the combined weight of a distribution’s tails relative to the center of the distribution. When a set of approximately normal data is graphed via a histogram, it shows a bell peak and most data within three standard deviations of the mean. However, when high kurtosis is present, the tails extend farther than the three standard deviations of the normal bell-curved distribution. A platykurtic distribution shows a negative excess kurtosis.

  • « Back to Glossary IndexIf your data demonstrates kurtosis, it is referring to the shape of your data distribution.
  • Data that follows a mesokurtic distribution shows an excess kurtosis of zero or close to zero.
  • In terms of shape, a leptokurtic distribution has fatter tails.
  • Statistic W may be viewed as the square of the correlation coefficient (i.e. the coefficient of determination) between the abscissa and ordinate of the normal probability plot described above.

B-Values for such modeling range from 1000s/mm2 to 3000s/mm2 and the number of distinct orientations is usually less than 100. Fiber orientations need not be discrete, because curvature and fanning of fibers can lead to a continuum of fiber orientations, and this is probably the case in most diffusion imaging voxels in the human brain. Of note, the ODF and the ADC profile are not the same thing. The ODF has been shown to have maxima along fiber orientations, and this is not necessarily the case for the ADC profile. The discrepancy arises because the ADC assumes a single Gaussian displacement distribution in the radial direction.

For investors, kurtosis is important in understanding tail risk, or how frequently “infrequent” events occur given one’s assumption about the distribution of price returns. Kurtosis explains how often observations in some data set fall in the tails vs. the center of a probability distribution. In finance and investing, excess kurtosis is interpreted as a type of risk, known as “tail risk,” or the chance of a loss occurring due to a rare event, as predicted by a probability distribution. When the continuous probability distribution curve is bell-shaped, i.e., it looks like a hill with a well-defined peak, it is said to be a normal distribution.

Skewness is a statistical numerical method to measure the asymmetry of the distribution or data set. It tells about the position of the majority of data values in the distribution around the mean value. Mesokurtic is the same as the normal distribution, which means kurtosis is near to 0. In Mesokurtic, distributions define kurtosis are moderate in breadth, and curves are a medium peaked height. Kurtosis is a statistical measure, whether the data is heavy-tailed or light-tailed in a normal distribution. The state or quality of flatness or peakedness of the curve describing a frequency distribution in the region about its mode.

So let us spend a few minutes talking about the shape of the normal distribution. Based on the predictions, advisors will advise the strategy and investment plan to the investor, and they will choose to go about the investment. There is a built-in function called Kurt in Excel To calculate Kurtosis in Excel. Where μ4 is the fourth central moment and σ is the standard deviation. Several letters are used in the literature to denote the kurtosis. A very common choice is κ, which is fine as long as it is clear that it does not refer to a cumulant.


Statistical and Mathematical software used is SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc. A large value of kurtosis indicates a more serious outlier issue and hence may lead the researcher to choose alternative statistical methods. The word “kurtosis” seems odd on the first or second reading. It actually makes sense, but we need to know Greek to recognize this.

define kurtosis

The data on daily wages of 45 workers of a factory are given. FREE INVESTMENT BANKING COURSELearn the foundation of Investment banking, financial modeling, valuations and more. A trick to remember the meaning of “platykurtic” is to think of a platypus with a thin tail. Structured Query Language What is Structured Query Language ? Structured Query Language is a specialized programming language designed for interacting with a database….

The first category of kurtosis is a mesokurtic distribution. This distribution has a kurtosis statistic similar to that of the normal distribution, meaning the extreme value characteristic of the distribution is similar to that of a normal distribution. In a normal distribution, data are symmetrically distributed with no skew. Most values cluster around a central region, with values tapering off as they go further away from the center.

Calculate the skewness coefficient of the sample

Taking all of this into consideration, one should consider that DWI and DTI are mature imaging techniques with several established brain applications, including ischemic stroke, brain tumors, and fiber tracking. DKI, although promising, still needs to be verified in its sensitivity and possible applications of its different metrics. What’s meant by “peakedness” is best understood from the example histograms shown below. Here are all the possible meanings and translations of the word kurtosis. On the estimation of the kurtosis in directional sea states for freak wave forecasting. The vertical axis is the maximum value of the kurtosis along the wave tank for different directional spreading , numerical results , and Eq.

Some authors and software packages use “kurtosis” by itself to refer to the excess kurtosis. For clarity and generality, however, this article explicitly indicates where non-excess kurtosis is meant. Like skewness, kurtosis is a statistical measure that is used to describe distribution.

Peakedness in a data distribution is the degree to which data values are concentrated around the mean. Datasets with high kurtosis tend to have a distinct peak near the mean and tend to decline rapidly, and have heavy tails. Datasets with low kurtosis tend to have a flat top near the mean rather than a sharp peak.

What Is Kurtosis? | Definition, Examples & Formula

In finance, a leptokurtic distribution shows that the investment returns may be prone to extreme values on either side. Therefore, an investment whose returns follow a leptokurtic distribution is considered to be risky. One looks for the largest deviation D between the cumulative empirical relative frequency distribution and the cumulative theoretical normal distribution. If D is larger than or equal to the critical value in the table, for a given number of observations n and significance level α, the hypothesis of normality is rejected. Greater values of K indicate higher degrees of peaked-ness whereas smaller K values indicate flatter distributions.

In probability theory and statistics, kurtosis is any measure of the “peakedness” of the probability distribution of a real-valued random variable. There are various interpretations of kurtosis, and of how particular measures should be interpreted; these are primarily peakedness, tail weight, and lack of shoulders. For this measure, higher kurtosis means more of the variance is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations. It is common practice to use an adjusted version of Pearson’s kurtosis, the excess kurtosis, to provide a comparison of the shape of a given distribution to that of the normal distribution.

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